School Supplies:
* Uniform:
* Three sets of plain work robes (black)
* One pointed hat (black) for day wear
* One pair of dress robes (black)
* One pair of sturdy plain shoes (black)
* One winter cloak (black with silver fastenings)
* One pair of gloves (leather or wool)
* One hat for winter wear (preferably warm)
* Books:
* The Standard Book of Spells, Grade 1
* Magical Theory
* A History of Magic
* Transfiguration Today
* The Dark Arts (This is a very controversial book, and Harry would have been better off without it!)
* One copy each of The Daily Prophet (for the first term) and the Quibbler
* Other:
* One wand (will be chosen for you at Ollivanders)
* One cauldron (pewter, standard size 2)
* One set of glass or crystal phials
* One telescope
* One set of scales
* One set of brass weights
* One set of ingredients for potions
* One quill (or a set of several)
* One ink bottle (black)
* One set of parchment
* One pair of owl nesting boxes
* One set of owl feeding equipment
* One owl (Harry didn't have this until later, but it's a very important part of the Hogwarts experience)
Optional Extras:
* A pet (Harry gets a rat, but there are other options like toads, cats, and owls)
* A trunk for storing your belongings (a magical trunk is recommended)
Things Harry doesn't know he needs:
* A map of the grounds: This is a very important item, although it's not listed as a requirement on the school list.
* A time-turner: This is a powerful, magical device that's not available to first-years (except for Hermione in the third book).
This list is from the first book, "Harry Potter and the Sorcerer's Stone." The exact requirements may change slightly in later books, but this is a good starting point.